Processing and traveltime inversion of seismic diffractions in anisotropic media

Abstract

Depth images based on seismic diffractions help identify heterogeneities in the subsurfacemissing in reflection-based sections. Diffractions also carry information from a wide rangeof wave-propagation directions, which can benefit anisotropic parameter estimation. One ofthe main challenges in utilizing diffraction events in imaging and velocity analysis is theirseparation from the more intensive reflections.Separation of diffractions can be achieved using the so-called specularity of seismic events,which is a measure of the deviation from Snell’s law. Here, I analyze two formulations ofspecularity suitable for anisotropic media and employ them to generate common-image gath-ers (CIGs) using the interface normal vectors obtained from migrated images. Applicationof a specially designed weighting function to these gathers suppresses reflections and allowsconstruction of diffraction-based depth images. Testing on a VTI (transversely isotropic witha vertical symmetry axis) ramp model demonstrates that both formulations of specularity,supplemented by appropriately designed weighting functions, produce satisfactory results fordiffraction separation in anisotropic media. The algorithms for separation and imaging ofdiffractions are successfully tested on the structurally complex VTI Marmousi model.In contrast to specularity gathers, dip-angle CIGs do not require information about reflectordips prior to migration and can also be effectively employed in diffraction imaging. Thesegathers are processed by applying dip-based muting functions followed by stacking along thedip axis. The effectiveness of this methodology in anisotropic diffraction imaging is demon-strated on synthetic data and a field data set from the Gulf of Mexico.Next, I study the influence of errors in the VTI parameters on reflection and diffractionevents in specularity and dip-angle gathers. Numerical examples show that the moveout ofdiffractions is particularly sensitive to the P-wave normal-moveout velocity V nmo and anellip-ticity parameter η (or V nmo and the horizontal velocity V hor ). In principle, diffractions in bothspecularity and dip-angle gathers could be employed in migration velocity analysis (MVA)to refine the anisotropic velocity model. However, the properties of diffraction moveout areshown to be different for CIGs shifted from the surface projections of the scatterers. Thiscomplicates application of MVA, which is based on the event flatness, to diffractions in thesegathers.Therefore, to incorporate diffractions into anisotropic velocity analysis, I develop traveltimetomography of diffraction arrivals in VTI media using the eikonal equation. The linearizedform of the eikonal equation is suitable for modeling of traveltime perturbations and com-puting the inversion gradients required by seismic tomography. I present an efficient androbust finite-difference (FD) methodology to solve the linearized eikonal equation for VTImedia. The accuracy of the proposed method is evaluated for Gaussian parameter anomaliesembedded in a homogeneous background and for the VTI Marmousi model. Traveltime to-mography is first performed for transmission data in a medium with Gaussian anomalies inthe velocities V nmo and V hor . Then the tomographic inversion for V nmo and V hor is applied todiffraction traveltimes from scatterers embedded in the Marmousi model. This experimentis repeated with noise-contaminated input traveltimes to evaluate the applicability of thealgorithm to field data. To produce geologically consistent velocity models, the inversiongradients are preconditioned with structure-oriented smoothing filters.